Supposedly the dealer already performed a balance and alignment when I took it into the shop a few days ago. (And this thread aside, I would have no reason to believe that they did not do it.)
Just because they did a tire balance doesn't mean they did it right. Typical tire balancing is done to a spec that is "close enough" (say a 1/4 ounce of weight or so) - this works from most cars, but the lighter a car is, and the less unsprung weight there is (tire/wheel/suspension components) the more the balancing becomes critical.
The more accurately you try to balance a tire, the longer it takes to do the job. Most shops get it "close enough". Close enough for an Explorer isn't close enough for an Elise.
As an example, in my old Elan, I always had a shimmy. Until I took it to a shop owned by and old man that was a perfectionist. He balanced my tires as close to perfect as it could possibly be, and there was absolute no shimmy. This was after several attempts to balance the tires using "computerized balancers".
Early Miatas also have a problem with being very sensitive to wheel balance, getting a shimmy around 60 MPH (it tends to go away by 70 or so) due to out of balance tires.
This might be a silly question, but should the purported flat spots be apparent to me after a visible inspection?
Not silly at all. But you aren't going to see a flat spot unless the tire is spinning on a machine - just looking at it isn't going to notice it being a couple of thousandths out of shape.
And should I be worried if they have done already performed a balance/alignment but it feels exactly the same?
Not worried. But they should do a better job, or find a shop that can do a better job. There is a particular machine called a "Road Force" balancer that does a good job on hard to balance tires/cars. It applies a rolling force to the tire as it would experience when it's running on the ground. They are purported to solve problems that other machines can't fix.
According to the Yokohama rep, the A048s and AD07s can both be permanently flat spotted by being exposed to cold temperatures while bearing the weight of the car. I was told that once the tires get below about 18 degrees that the physical properties of the rubber will change and the flat spots may not necessarily go away even after being brought back up to temp.
Yes and no. The real problem is that if you attempt to use the tire when it's cold and deformed, it will have a problem - cracking the internal sidewall structure and such.
They've later alluded to the fact that the car just sitting on the tires (car not being used) won't really do any damage.